{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 24\n",
    "\n",
    "# 拟合，无截距\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abd1cc37-d3c4-4185-b7e1-faf17e3a1b00",
   "metadata": {},
   "source": [
    "该代码主要用于通过最小二乘法来拟合数据并可视化拟合的结果。在这里，我们有两种动物的数量数据：鸡和兔子，数据存储在数组`num_chickens`和`num_rabbits`中。通过建立一个线性模型，目标是找到一个最佳的斜率$a$，使得模型的预测值能够尽可能接近实际观察到的兔子数量。\n",
    "\n",
    "首先，我们定义了一个预测函数$y_{\\text{pred}}$，表示兔子的数量与鸡的数量之间的线性关系，即：\n",
    "\n",
    "$$y_{\\text{pred}} = a \\cdot x_{\\text{chickens}}$$\n",
    "\n",
    "接下来，通过计算每个鸡数量对应的兔子数量的误差平方和（Sum of Squared Errors，SSE），并用符号计算得到$SSE$的表达式：\n",
    "\n",
    "$$SSE(a) = \\sum_{i=1}^{n} (y_{\\text{rabbits}}[i] - a \\cdot x_{\\text{chickens}}[i])^2$$\n",
    "\n",
    "代码中使用SymPy库来进行符号计算，以便在不同的$a$值下计算$SSE$的值，找到使得$SSE$最小的$a$值。\n",
    "\n",
    "在计算出最佳的$a$后，我们绘制了鸡的数量与兔子的数量之间的关系图。在图中，使用红色线条表示预测的兔子数量，同时标记出实际的散点数据。为每个散点数据绘制矩形，以显示它们与预测值之间的差异。这种表示方式有助于我们更直观地理解模型的拟合效果和残差的大小。\n",
    "\n",
    "最后，输出最优解和对应的误差，进一步验证模型的准确性和可靠性。整个过程可以清楚地反映出如何利用线性回归分析来进行数据建模及预测。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6f35b20c-d6ad-4013-91c0-f0687dad9f8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.abc import a  # 导入符号变量 a\n",
    "import numpy as np  # 导入 NumPy 库\n",
    "import matplotlib.pyplot as plt  # 导入 Matplotlib 库用于绘图"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1fc24e8-80f8-4ed2-9220-d39db42511f9",
   "metadata": {},
   "source": [
    "## 定义绘图装饰函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0e108c33-e31a-429e-8c1f-7360c5414fde",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fig_decor(ax):  # 定义绘图装饰函数\n",
    "    plt.xlabel('$x$ (number of chickens)')  # 设置 x 轴标签\n",
    "    plt.ylabel('$y$ (number of rabbits)')  # 设置 y 轴标签\n",
    "    plt.axis('scaled')  # 使 x 和 y 轴比例相同\n",
    "    ax.set_xlim([0, 120])  # 设置 x 轴范围\n",
    "    ax.set_ylim([0, 80])  # 设置 y 轴范围\n",
    "    plt.xticks(np.arange(0, 120 + 1, step=10))  # 设置 x 轴刻度\n",
    "    plt.yticks(np.arange(0, 80 + 1, step=10))  # 设置 y 轴刻度\n",
    "    plt.minorticks_on()  # 打开次刻度\n",
    "    ax.grid(which='minor', linestyle=':', linewidth='0.5', color=[0.8, 0.8, 0.8])  # 设置次刻度网格\n",
    "    ax.spines['top'].set_visible(False)  # 隐藏上边框\n",
    "    ax.spines['right'].set_visible(False)  # 隐藏右边框\n",
    "    ax.spines['bottom'].set_visible(False)  # 隐藏下边框\n",
    "    ax.spines['left'].set_visible(False)  # 隐藏左边框\n",
    "    ax.grid(linestyle='--', linewidth=0.25, color=[0.5, 0.5, 0.5])  # 设置主网格"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "198cb1ff-0607-4c57-97e8-5e671b829a8f",
   "metadata": {},
   "source": [
    "## 生成数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "961cb975-87a8-483f-b0ee-a9b5c138b43d",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chickens = np.array([32, 110, 71, 79, 45, 20, 56, 55, 87, 68, 87, 63, 31, 88])  # 鸡的数量\n",
    "num_rabbits  = np.array([22, 53, 39, 40, 25, 15, 34, 34, 52 , 41, 43, 33, 24, 52])  # 兔子的数量"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8117dc66-2bd2-482f-ad0d-57e07f26d5bf",
   "metadata": {},
   "source": [
    "## 散点图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0b0fa3d5-5907-41a4-9125-b0471120c337",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()  # 创建子图\n",
    "plt.scatter(num_chickens, num_rabbits)  # 绘制散点图\n",
    "fig_decor(ax)  # 应用图形装饰"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a4ed8a6a-7963-4070-8572-58e395d5b94b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 生成 f(a)，最小二乘误差（SSE），符号表示\n",
    "from sympy import *  # 导入符号计算库\n",
    "\n",
    "y_pred = a*num_chickens  # 预测值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "efa6ea41-0025-4996-a677-6e40cf9ba224",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "65428*a**2 - 72228*a + 20179\n"
     ]
    }
   ],
   "source": [
    "f_a_SSE = np.sum((num_rabbits - y_pred)**2)  # 计算误差平方和\n",
    "f_a_SSE = simplify(f_a_SSE)  # 简化表达式\n",
    "print(f_a_SSE)  # 输出 SSE 表达式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a3e375be-c0c7-4564-b4a3-ac6a311ab356",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 绘制 f(a) 与 a 的关系\n",
    "a_array = np.linspace(0,1,51)  # 创建 a 的值范围"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "42514a6b-b25c-4ed8-840d-bc4c34b517b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_a_SSE_fcn = lambdify(a, f_a_SSE)  # 将 SSE 函数转化为可计算的函数\n",
    "SSE_array = f_a_SSE_fcn(a_array)  # 计算不同 a 值下的 SSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1857155f-b9ea-45fe-a928-7f9908b76eea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "130856*a - 72228\n"
     ]
    }
   ],
   "source": [
    "# 一阶导数\n",
    "df_da_SSE = diff(f_a_SSE, a)  # 计算一阶导数\n",
    "print(df_da_SSE)  # 输出一阶导数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "59ea9280-3726-48f6-97ba-334f2371e157",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[18057/32714]\n"
     ]
    }
   ],
   "source": [
    "# 解 a 的值\n",
    "a_star_only = solve(df_da_SSE, a)  # 求解使一阶导数为零的 a 值\n",
    "print(a_star_only)  # 输出解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7c39a4f2-0ff3-49b0-b749-cf46be10b4e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "a_star_only = a_star_only[0].evalf()  # 计算 a 的数值解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "214bb165-56fa-40ba-b9c5-a3ac7176f068",
   "metadata": {},
   "outputs": [],
   "source": [
    "SSE_min = f_a_SSE_fcn(a_star_only)  # 计算最小 SSE 值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f1ea37d7-28fa-402d-94a4-db97319fd196",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()  # 创建子图\n",
    "plt.plot(a_array, SSE_array)  # 绘制 SSE 随 a 的变化\n",
    "plt.axvline(x=a_star_only, linestyle='--')  # 绘制 a 的最优解线\n",
    "plt.plot(a_star_only, SSE_min, 'rx', markersize=16)  # 绘制最优解点\n",
    "\n",
    "plt.xlabel('a, slope')  # 设置 x 轴标签\n",
    "plt.ylabel('f(a), sum of squared errors, SSE')  # 设置 y 轴标签\n",
    "ax.set_xlim([a_array.min(), a_array.max()])  # 设置 x 轴范围\n",
    "ax.set_ylim([0, SSE_array.max()])  # 设置 y 轴范围\n",
    "\n",
    "ax.grid(linestyle=':', linewidth='0.5', color=[0.8, 0.8, 0.8])  # 设置网格\n",
    "\n",
    "ax.spines['top'].set_visible(False)  # 隐藏上边框\n",
    "ax.spines['right'].set_visible(False)  # 隐藏右边框"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6173af93-3154-4c1d-9838-c2e8a00c78f8",
   "metadata": {},
   "source": [
    "## y = ax 模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5ddaaf9b-192c-4e8f-9412-a8f3a61ce8b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_square(x,y1,y2):  # 定义绘制矩形的函数\n",
    "    if y2 > y1:  # 确保 y2 是较小的值\n",
    "        temp = y2\n",
    "        y2 = y1\n",
    "        y1 = temp\n",
    "\n",
    "    d = y1 - y2  # 计算高差\n",
    "\n",
    "    plt.fill(np.vstack((x, x + d, x + d, x)), \n",
    "             np.vstack((y2, y2, y1, y1)),\n",
    "             facecolor='b', edgecolor='none',\n",
    "             alpha=0.3)  # 绘制矩形"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ec9e0368-054b-4489-babd-7cd2bc0d51eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_array = np.linspace(0,150,10)[:, None]  # 创建 x 的值范围"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ea5c04df-262e-45f9-b5dd-dab195c7bfaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = a_star_only*x_array  # 计算预测值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "09243d90-75d7-43d4-901f-03d86957b6a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()  # 创建子图\n",
    "\n",
    "plt.plot(x_array, y_pred, color='r')  # 绘制预测的线\n",
    "plt.scatter(num_chickens, num_rabbits)  # 绘制散点图\n",
    "\n",
    "num_rabbits_predicted = a_star_only*num_chickens  # 计算预测的兔子数量\n",
    "\n",
    "plt.plot(np.vstack((num_chickens,num_chickens)),\n",
    "         np.vstack((num_rabbits, num_rabbits_predicted)),\n",
    "         color=np.array([255,182,0])/255)  # 绘制预测线\n",
    "\n",
    "for i in range(0,len(num_rabbits_predicted)):  # 绘制每个点的矩形\n",
    "    plot_square(num_chickens[i],num_rabbits[i],num_rabbits_predicted[i]); \n",
    "\n",
    "fig_decor(ax)  # 应用图形装饰"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
